Stocks climbed, supported by a stunning jobs report from the private sector, raising hopes for a strong nonfarm payroll data on Friday.

The Dow Jones Industrial Average gained 31.71 points, or 0.27 percent, to close at 11.722.89.The S&P 500 index rose 6.36 points, or 0.50 percent, to 1276.56; and the Nasdaq added 20.95 points, or 0.78 percent, at 2702.20.

Payroll processor ADP reported that the private sector payrolls surged by 297,000 in December (far ahead of expectations). Also, outplacement firm Challenger Gray & Christmas reported that job cuts dropped by 59 percent to 530,000 in 2010 -- the lowest level in 13 years.

Moreover, the Institute of Supply Management showed that activity in the service sector rose in December -- the related index rose to 57.1 in December, up from 55 in November. A reading above 50 signals expansion.

Qualcomm (Nasdaq: QCOM) agreed to buy chip-maker Atheros Communications (ATHR) for $3.1 billion in cash, or $45 per share.

Oil futures rose more than 1 percent to close at $90.35 per barrel. Gold futures slipped.

Bonds fell, as the yield on the 10-Year Treasury rose to 3.48 percent.